The Rockets sent Motiejunas and guard Marcus Thornton to the Pistons on Thursday for a protected 2016 first-round pick.
But Motiejunas, who hasn't played in an NBA game since Dec. 31 because of his recovery from a sore back, is getting looked at closely by Pistons medical officials.
Pistons coach Stan Van Gundy told reporters after Sunday's loss to the Pelicans that the NBA granted Detroit's request for an extension to complete the trade. The Pistons had asked the league for an additional 24 hours to the 72-hour trade window to determine if Motiejunas can play for them.
The Pistons and Rockets have until 6 p.m. ET on Monday to finalize the deal, according to Van Gundy.
Motiejunas has played in a handful of D-League games for the Rockets since Dec. 31 and was on target to participate in NBA games again, including last Friday's game at Phoenix.
Motiejunas underwent back surgery late last season and suffered several setbacks during his recovery.
If the deal is voided, it would be a major disappointment to the Rockets, who valued acquiring a first-round pick at the trade deadline as the source for any deal.